Here are two links that discuss TC characters,
http://www.cactusgamedesign.com/message_boards/ruling-questions/territory-class/
http://www.cactusgamedesign.com/message_boards/ruling-questions/tc-character-abilities/
From what I understand their abilities only activate when they enter territory, or battle.
2. Yes, he has reentered territory his ability reactivates.
For 1. I am guessing that the negate wears off after battle phase, if not, you can put them in battle, and when they hit territory again, they will reactivate.
3. Yes, same reasoning as 2.
4. Yes, TC abilities will activate in battle and when they hit territory, whether from hand or battle.